Evaluation of Formative
5.4 Case Study Illustration: Formative Measurement Models
5.4.1 Model Setup and Estimation
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the constructs and their relationships, which represent the extended structural model for our PLS-SEM example in the remaining chapters of the book. To sum- marize, the extended corporate reputation model has three main conceptual/theo- retical components:
1. The target constructs of interest (CUSA and CUSL)
2. The two corporate reputation dimensions, COMP and LIKE, that represent key determinants of the target constructs
3. The four exogenous driver constructs (i.e., ATTR, CSOR, PERF, and QUAL) of the two corporate reputation dimensions
The endogenous constructs on the right-hand side in .Fig. 5.3 include a single- item construct (i.e., CUSA) and three reflectively measured constructs (i.e., COMP, CUSL, and LIKE). In contrast, the four new driver constructs (i.e., exogenous latent variables) on the left-hand side of .Fig. 5.3 (i.e., ATTR, CSOR, PERF, and QUAL) have formative measurement models in accordance with their role in the reputation model (Schwaiger, 2004). Specifically, the four new constructs are measured by a total of 21 formative indicators (detailed in .Table 5.3) that have been derived from literature, qualitative studies, and quantitative pretests (for more details, see Schwaiger, 2004). .Table 5.3 also lists the single-item reflective global measures for validating the formative driver constructs when executing the redundancy analysis.
We continue to use the corp_rep_data dataset with 344 observations intro- duced in 7Chap. 3 for our PLS-SEM analyses. Unlike in the simple model that was used in the previous chapter, we now also have to consider the formative measure- ment models when deciding on the minimum sample size required to estimate the model. The maximum number of arrowheads pointing at a particular construct occurs in the measurement model of QUAL. All other formatively measured con- structs have fewer indicators. Similarly, there are fewer arrows pointing at each of the endogenous constructs in the structural model. Therefore, when building on the 10-time rule of thumb, we would need 8 · 10 = 80 observations. Alternatively, fol- lowing Cohen’s (1992) recommendations for multiple ordinary least squares regres- sion analysis or running a power analysis using the G*Power program (Faul, Erdfelder, Buchner, & Lang, 2009), we would need only 54 observations to detect R2 values of around 0.25, assuming a significance level of 5% and a statistical power of 80%. When considering the more conservative approach suggested by Kock and Hadaya (2018), we obtain a higher minimum sample size. Considering prior research on the corporate reputation model, we expect a minimum path coefficient of 0.15 in the structural model. Assuming a significance level of 5% and statistical power of 80%, the inverse square root method yields a minimum sample size of approxi- mately 155 (see 7Chap. 1 for a discussion of sample size and power considerations).
The corporate reputation data can be accessed by the object name corp_rep_data:
# Load the SEMinR library library(seminr)
# Load the corporate reputation data corp_rep_data <- corp_rep_data
Chapter 5 · Evaluation of Formative Measurement Models
.Table 5.3 The indicators of the formatively measured constructs
Quality (QUAL)
qual_1 The products/services offered by [the company] are of high quality
qual_2 [The company] is an innovator, rather than an imitator with respect to [industry]
qual_3 [The company]’s products/services offer good value for money qual_4 The products/services offered by [the company] are good qual_5 Customer concerns are held in high regard at [the company]
qual_6 [The company] is a reliable partner for customers qual_7 [The company] is a trustworthy company qual_8 I have a lot of respect for [the company]
Performance (PERF)
perf_1 [The company] is a very well-managed company perf_2 [The company] is an economically stable company
perf_3 The business risk for [the company] is modest compared to its competitors perf_4 [The company] has growth potential
perf_5 [The company] has a clear vision about the future of the company Corporate social responsibility (CSOR)
csor_1 [The company] behaves in a socially conscious way
csor_2 [The company] is forthright in giving information to the public csor_3 [The company] has a fair attitude toward competitors
csor_4 [The company] is concerned about the preservation of the environment csor_5 [The company] is not only concerned about profits
Attractiveness (ATTR)
attr_1 [The company] is successful in attracting high-quality employees attr_2 I could see myself working at [the company]
attr_3 I like the physical appearance of [the company] (company, buildings, shops, etc.) Single-item measures of QUAL, PERF, CSOR, and ATTR for the redundancy analysis qual_global Please assess the overall quality of [the company’s] activities
perf_global Please assess [the company’s] overall performance
csor_global Please assess the extent to which [the company] acts in socially conscious ways attr_global [The company] has a high overall attractiveness
Source: Hair et al., 2022, Chap. 5; used with permission by Sage 5.4 · Case Study Illustration: Formative Measurement Models
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The extended corporate reputation model’s structural and measurement models will have to be specified using the SEMinR syntax. Remember that the four drivers are formative constructs, estimated with mode_B, while COMP, CUSL and LIKE are reflective constructs, estimated with mode_A. The weights parameter of the composite() function is set by default to mode_A. Thus, when no weights are specified, the construct is estimated as being reflective. Alternatively, we can explic- itly specify the mode_A setting for reflectively measured constructs or the mode_B setting for formatively measured constructs. Once the model is set up, we use the estimate_pls() function to estimate the model, this time specifying the mea- surement_model and structural_model parameters to the extended corporate reputation model objects (corp_rep_mm_ext, corp_rep_sm_ext). Finally, we apply the summary() function to the estimated SEMinR model object corp_rep_
pls_model_ext and store the output in the summary_corp_rep_ext object:
# Create measurement model corp_rep_mm_ext <- constructs(
composite(“QUAL”, multi_items(“qual_”, 1:8), weights = mode_B),
composite(“PERF”, multi_items(“perf_”, 1:5), weights = mode_B),
composite(“CSOR”, multi_items(“csor_”, 1:5), weights = mode_B),
composite(“ATTR”, multi_items(“attr_”, 1:3), weights = mode_B),
composite(“COMP”, multi_items(“comp_”, 1:3)), composite(“LIKE”, multi_items(“like_”, 1:3)), composite(“CUSA”, single_item(“cusa”)), composite(“CUSL”, multi_items(“cusl_”, 1:3)) )# Create structural model
corp_rep_sm_ext <- relationships(
paths(from = c(“QUAL”, “PERF”, “CSOR”, “ATTR”), to = c(“COMP”, “LIKE”)),
paths(from = c(“COMP”, “LIKE”), to = c(“CUSA”, “CUSL”)), paths(from = c(“CUSA”), to = c(“CUSL”))
)# Estimate the model
corp_rep_pls_model_ext <- estimate_pls(
data = corp_rep_data,
measurement_model = corp_rep_mm_ext, structural_model = corp_rep_sm_ext, Excurse
The corporate reputation data file and project are also bundled with SEMinR. Once the SEMinR library has been loaded, we can access the demonstration code for 7Chap. 5 by using the demo() function on the object “seminr-primer- chap5”.
Chapter 5 · Evaluation of Formative Measurement Models
missing = mean_replacement, missing_value = “-99”)
# Summarize the model results
summary_corp_rep_ext <- summary(corp_rep_pls_model_ext)
Just like the indicator data that we used in previous chapters, the corp_rep_data dataset has very few missing values. The number of missing observations is reported in the descriptive statistic object nested within the summary return object. This report can be accessed by inspecting the summary_corp_rep_
ext$descriptives$statistics object. Only the indicators cusl_1 (three miss- ing values, 0.87% of all responses on this indicator), cusl_2 (four missing values, 1.16% of all responses on this indicator), cusl_3 (three missing values, 0.87% of all responses on this indicator), and cusa (one missing value, 0.29% of all responses on this indicator) include missing values. Since the number of missing values is rela- tively small (i.e., less than 5% missing values per indicator; Hair et al., 2022, Chap.
2), we use mean value replacement to deal with missing data when running the PLS-SEM algorithm (see also Grimm & Wagner, 2020).
When the PLS-SEM algorithm stops running, check whether the algorithm converged (Hair et al., 2022, Chap. 3). For this example, the PLS-SEM algorithm will stop when the maximum number of 300 iterations or the stop criterion of 1.0E-7 (i.e., 0.0000001) is reached. To do so, it is necessary to inspect the corp_
rep_pls_model object by using the $ operator:
# Iterations to converge
summary_corp_rep_ext$iterations
The results show that the model estimation converged after eight iterations. Next, the model must be bootstrapped to assess the indicator weights’ significance. For now, we run a simple bootstrap as conducted in 7Chap. 4. But in this chapter, we discuss the bootstrap function in further detail when assessing the formative indi- cator weights’ significance. To run the bootstrapping procedure in SEMinR, we use the bootstrap_model() function and assign the output to a variable; we call our variable boot_corp_rep_ext. Then, we run the summary() function on the boot_corp_rep object and assign it to another variable, such as sum_boot_
corp_rep_ext.
# Bootstrap the model
boot_corp_rep_ext <- bootstrap_model(
seminr_model = corp_rep_pls_model_ext, nboot = 1000)
# Store the summary of the bootstrapped model
sum_boot_corp_rep_ext <- summary(boot_corp_rep_ext, alpha = 0.10)
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